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%I #10 May 02 2017 11:35:48
%S 0,0,0,1,3,2,5,2,4,4,2,5,6,4,4,6,4,3,6,5,4,6,4,8,7,6,5,6,6,9,6,7,8,5,
%T 8,6,7,10,5,9,8,6,6,7,10,7,9,9,6,9,12,11,7,8,11,8,11,8,11,12,9,11,13,
%U 9,10,14,13,13,7,9,12,12,12,14,11,11,15,13,15,12,13,9,12,12,13,14,13,14,13
%N Number of representations of n-th prime of the form p1*p2+p3, where p1, p2 and p3 are primes, not necessarily all distinct.
%C a(n) = Sum(A064911(A000040(n)-A000040(k)): 1<=k<n). - _Reinhard Zumkeller_, Sep 22 2005
%H Michael De Vlieger, <a href="/A112528/b112528.txt">Table of n, a(n) for n = 1..1000</a>
%e No solutions for 2,3,5;
%e 7=2*2+3, 11=2*2+7=2*3+5=3*3+2, 13=2*3+7=2*5+3, 17=2*2+13=2*3+11=2*5+7=2*7+3=3*5+2,
%e 19=2*3+13, 23=2*2+19=2*3+17=2*5+13=3*7+2, 29=2*3+23=2*5+19=2*11+7=2*13+3,
%e 31=2*7+17=2*13+5, ...
%t Table[Function[q, Length@ DeleteCases[#, s_ /; Length@s != 3] &@ Map[Flatten[ FactorInteger[#] /. {{p_, e_} /; p > 1 :> ConstantArray[p, e], {1, 1} -> 1}] &, Select[IntegerPartitions[q, {2}], And[! MemberQ[#, 1], Total@ Boole@ PrimeQ@ # == 1] &]]]@ Prime@ n, {n, 89}] (* _Michael De Vlieger_, May 01 2017 *)
%K nonn
%O 1,5
%A _Zak Seidov_, Sep 10 2005
%E More terms from _Reinhard Zumkeller_, Sep 22 2005
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